A Bayesian Exploration on Scooby Doo Villain Unmasking

Fear Prior Distribution

• Rationale:
  Fear is not confident about the probability of unmasking, so \(\pi\) can be set as \(0.50\). Considering Fear is not confident about his answer, the his distribution will have a wide shape, large variance. We picked \(\alpha = 2\) and \(\beta=2\) such that \(\pi=0.50\) and \(V[\pi]=0.50\), based on the beta distribution expectation: \(E[\pi]= \frac{\alpha}{\alpha + \beta}\)

Ennui Prior Distribution

• Rationale:
  Ennui shrugs when asked each question, which means that there is not much information from her. That is, we are uncertain about her thought about \(\pi\).

Joy Prior Distribution

• Rationale:
  Joy is very certain about the unmasking, and very confident about her answer, so I set the expectation of \(\pi\) to \(0.90\) by setting \(\alpha=9\) and \(\beta=1\).

Villain Motive Theft: Fear Iteration

Villain Motive Theft: Ennui Iteration

Villain Motive Theft: Joy Iteration

Prior and motive impact on the posterior: Villain Motive Theft

Villain Motive Competition

Summary of Competition Motive Episodes:

Fear Prior’s and Posteriors for Competition Motive Episodes:

Joy Prior’s and Posteriors for Competition Motive Episodes:

Ennui Prior’s and Posteriors for Competition Motive Episodes:

Evolution of the posteriors of all 3 emotions in Competition Motive Episodes over the decades:

Villain Motive Power

Villain Motive Power: Fear Iteration

Villain Motive Power: Ennui Iteration

Villain Motive Power: Joy Iteration

Prior and motive impact on the posterior: Villain Motive Power

Villain Motive Greed

Fear

Fear

Ennui

Ennui

Joy

Joy

Summary